We know that if S is a subsemigroup of a semitopological semigroup T , and 𝔉 stands for one of the spaces 𝒜 𝒫 , 𝒲 𝒜 𝒫 , 𝒮 𝒜 𝒫 , 𝒟 or ℒ 𝒞 , and ( ϵ , T 𝔉 ) denotes the canonical 𝔉 -compactification of T , where T has the property that 𝔉 ( S ) = 𝔉 ( T ) | s , then ( ϵ | s , ϵ ( S ) ¯ ) is an 𝔉 -compactification of S . In this paper, we try to show the converse of this problem when T is a locally compact group and S is a closed normal subgroup of T . In this way we construct various semigroup compactifications of T from the same type compactifications of S .